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Popular >

sqrt(2)cos(45)

Solution

2 cos (4 5^{\circ})

Solution

1

Solution steps

2 cos (4 5^{\circ})

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

= 2 \frac{2}{2}

Simplify

2 \frac{2}{2} : 1

2 \frac{2}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 2}{2}

22 = 2

22

Apply radical rule:

a a = a

22 = 2

= 2

= \frac{2}{2}

Apply rule

\frac{a}{a} = 1

= 1

= 1

Popular Examples

sin((7pi)/(11))

sin (\frac{7 π}{11})

3cos(45)tan(60)-cos(15)

3 cos (4 5^{\circ}) tan (6 0^{\circ}) - cos (1 5^{\circ})

2 \cdot (cos (4 5^{\circ}))^{2}

sin(arctan(3/8))

sin (arctan (\frac{3}{8}))

-0.208+(5/4 sin^2(0.5)-5/12)0.5

- 0.208 + (\frac{5}{4} sin^{2} (0.5) - \frac{5}{12}) 0.5

Frequently Asked Questions (FAQ)

What is the value of sqrt(2)cos(45) ?
The value of sqrt(2)cos(45) is 1